I don't know if anyone else is interested in this topic, but as PADT mentions, its a common inquiry.
So, I found a method that works to extract the 6 degrees of freedom as relative displacements (3 rotations, 3 translations). In the test case of a cantilever beam in bending with a translating base, the user can insert a General Joint with all degrees of freedom set to free. Define contacts as usual (for example, a bonded connection between base and beam). Create remote points; one at the connection between bodies and one at the free end (or location of choice). Set the joint to be defined by these remote points. You will need to choose a newly defined coordinate system for these remote points that have 0,0,0 coordinates at the chosen locations. Make sure Joint Behavior is set to deformable. When solve is complete, use Joint Probe for any chosen degree of freedom by the Relative options.
Unfortunately, this does require some pre-planning or resolving but it does allow the user to define the coordinates in which they want their relative results, which PADT's solution does not allow.
Heres the setup:
Time Step 1: Apply end load, F = 1000N (beam geometry: 70mm Length, 10x10mm cross section; structural steel default)
Time Step 2: Apply end load + base displacement of -0.2mm in X and -0.125mm in Y (arbitrary amounts).
As expected, ANSYS combines those translations of TS2 into the directional deformation. TS1 shows only the strain based deflection (plus some small elastic interaction at the base im assuming since the analytical solution is 0.686mm).
When using the Joint Probe method as proposed, the analytical solution is constant through all time steps regardless of the base translations that I prescribed from the displacment loading.

Ideally this method should be able to be used for any geometry, but I would be careful to check a test case. Any degree of freedom should be able to be probed for relative results now.

Any reason this might not be a good solution for Relative Displacements?